It is possible to place a catalyst suitable for the reduction of NOx in an exhaust gas by ammonia and to feed an aqueous urea solution into the engine exhaust passage upstream of the catalyst to cause reduction of the NOx in exhaust gas by the ammonia generated from the aqueous urea solution. In this case, however, the purification rate of the NOx becomes lower along with a fall in the temperature of the catalyst. Therefore, known in the art has been an internal combustion engine designed to calculate the equivalent ratio of the urea necessary for reducing NOx by an NOx purification rate in accordance with the catalyst temperature and to control the amount of feed of the aqueous urea solution so that urea is fed by that equivalent ratio (see Japanese Unexamined Utility Model Publication (Kokai) No. 3-129712).
So long as feeding urea by an equivalent ratio calculated in this way, however, when the catalyst temperature is not that high, the NOx purification rate is low. Therefore, when the catalyst temperature is not that high, there is the problem that a high NOx purification rate cannot be obtained. In particular, when the catalyst temperature does not become that high and the amount of NOx in the exhaust gas is large, such as when the engine is accelerating from a low load operating state, if the NOx purification rate is low, the problem will arise of a large amount of NOx being released into the atmosphere.